Can I style the widget output?

Absolutely! The widget area will have an id of "latest-spotify-activity". You can style the inner html by adding styles specific to the ID like '#latest-spotify-activity h3', '#latest-spotify-activity p' & '#latest-spotify-activity abbr'. This plugin will inherit your previously existing widget styling if you don't specify any specific to the widget.

Does it auto-scroll line in facebook?

No. There is no javascript called or integrated with this plugin whatsoever, in order to keep resource usage as low as possible. This means it does not auto-populate new data like facebook does. This widget is intended to simply allow somebody to view your latest activity at the time of opening your page/post. Each time you switch/open/reload pages, the widget shows your most recent Spotify activity.

Will it display new song data even if my pages having caching turned on?

This depends on how in-depth your caching is. If you're caching everything, even HTML, it's failing approx 1:10 times. No page caching = 100% success rate. I will work on a solution for people who are caching their html, in a future version.